Transient convective spin-up dynamics

Melting driven by rotating Rayleigh–Bénard convection

“…2012), the latter finding . For more modest values of , Ravichandran & Wettlaufer (2020) found and Liu & Ecke (2009) found . In the limit of large , that is in the classical non-rotating Rayleigh–Bénard convection regime, one finds, with a different prefactor than in (3.8), up to (Doering, Toppaladoddi & Wettlaufer 2019; Doering 2020 a , b ; Iyer et al.…”

“…For large values of Ra/Ra bulk c , two values have been suggested in the literature; β = 3 (Boubnov & Golitsyn 1990;King et al 2012) and β = 3/2 (Julien et al 2012), the latter finding C = (1/25)Pr −1/2 . For more modest values of Ra/Ra bulk c , Ravichandran & Wettlaufer (2020) found β = 3/4 and Liu & Ecke (2009) found β = 2/7. In the limit of large Ro, that is in the classical non-rotating Rayleigh-Bénard convection regime, one finds, with a different prefactor than in (3.…”

“…No-slip conditions are also applied at the freely evolving phase boundary, where the temperature is . Ravichandran & Wettlaufer (2020) showed that free-slip boundaries support flow structures that no-slip boundaries cannot. Here, in order to examine how such structures influence the melting dynamics, a free-slip velocity condition is used on the lower boundary, except in § 3.2.1, where we study the influence of the no-slip velocity boundary condition on the lower boundary.…”

“…Equations ((2.16) and (2.17)), together with (2.19), are solved using the finite volume solver Megha-5 on a uniform grid in all three space directions (Diwan et al. 2014; Prasanth 2014; Ravichandran & Wettlaufer 2020; Ravichandran, Meiburg & Govindarajan 2020). After every time step of (2.16) and (2.17), an equilibration step is implemented using (2.10) and (2.11).…”

The combined effects of buoyancy, rotation, and shear on phase boundary evolution

“…Equations 11 -13, along with the boundary conditions, are solved using the finite-volume solver Megha-5, with a volume penalization method for the melting solid. The solver uses second-order central differences in space and a second-order Adams-Bashforth time-stepping scheme, and has been extensively validated for free-shear flows [44,45] and Rayleigh-Bénard convection [41,46,47]. Details of the volume-penalization algorithm, including validation against the analytical solution for the purely conductive Stefan problem, tests of sensitivity to the penalization parameter, and the convergence of the solution under grid-refinement may be found in Ravichandran and Wettlaufer [41].…”